E3 — BOSS CMASS × Planck lensing/tSZ (tiled shell)
Setup: CMASS-North, z ∈ [0.45, 0.55] (291188 galaxies; 274075 used across 18 tiles of 512 Mpc/h at 4 Mpc/h voxels). Spines at matched length (2400 vox per tile), both methods. Stacks: mean map value at spine sky positions vs 200 footprint-constrained RA-rotated/DEC-reflected controls. First pass: no systematics weights, single shell, projected through the full shell depth.
M3 on real data (spine–tidal-frame alignment, null 0.5)
- hessian: 0.617 ± 0.016 (mean ± sd over tiles)
- se3_lift: 0.677 ± 0.016 (mean ± sd over tiles)
Cross-signal stacks
| spine set | map | stack | null mean ± std | SNR |
|---|---|---|---|---|
| hessian | kappa | 1.078e-03 | -9.332e-04 ± 5.979e-03 | 0.34 |
| hessian | y | 4.517e-08 | -2.951e-08 ± 1.549e-08 | 4.82 |
| se3_lift | kappa | -1.400e-03 | -6.835e-05 ± 5.940e-03 | -0.22 |
| se3_lift | y | 3.343e-08 | -2.487e-08 ± 1.409e-08 | 4.14 |
Reading: positive SNR means the spine network sits on more lensing convergence / hot gas than footprint-matched random placements. H3 asks whether the lift’s spines carry at least the Hessian’s signal at equal length.
Verdict (first pass)
- H3 — spine networks trace real gas: supported. Both methods’ spine networks show a ~4–5σ Compton-y excess over footprint-matched controls; Planck lensing is null (noise-dominated at these scales, as expected).
- H3 comparison — Hessian ≥ lift on real cross-signals (4.8σ vs 4.1σ at matched length), consistent with the corrected H1 and E1b: the simpler model is also the better mass/gas tracer on real data.
- M3-real — the lift’s descriptor advantage replicates on the real Universe: spine–tidal-frame alignment 0.677 ± 0.016 vs 0.617 ± 0.016 across 18 independent tiles (null 0.5) — a clean, tile-replicated separation matching the simulation finding.
Caveats (would tighten a second pass)
- Controls rotate in RA / reflect in DEC, which changes galactic latitude; a latitude-dependent y foreground could bias the SNR. Fixed-galactic- latitude nulls are the right refinement.
- The y excess includes the halo gas of the CMASS tracers themselves, not only intergalactic filament gas; masking tracer positions would isolate the WHIM component.
- No FKP/systematics weights; single redshift shell; spines projected through the full ~250 Mpc/h shell depth.